Speaking after the result was declared in Liverpool, Corbyn thanked his rival, Owen Smith, and urged the “Labour family” to unite after the summer-long contest.

“We have much more in common than that which divides us,” he said. “Let’s wipe that slate clean from today and get on with the work we’ve got to do as a party together.”

Corbyn secured 61.8% of the vote to Smith’s 38.2%. The victory strengthens his hold on a party that has expanded dramatically since the 2015 general election and now has more than 500,000 members. In last year’s contest, he won 59.5% of the vote.

Corbyn won a majority over Smith in every category – members (59%), registered supporters (70%) and trades union affiliates (60%).

The winner pointed out that he had secured his second mandate in a year and urged his colleagues to accept what had been a democratic decision.

What next for Jeremy Corbyn?

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Smith congratulated Corbyn for mobilising so many supporters in the party, and said he would reflect on how he could help Labour to win the next election.

He said: “I entered this race because I didn’t think Jeremy was providing the leadership we needed, and because I felt we must renew our party to win back the voters’ trust and respect. However, I fully accept and respect the result and I will reflect carefully on it and on what role I might play in future to help Labour win again for the British people.”

That is likely to be read as a hint that the former shadow work and pensions secretary might be willing to accept a frontbench role, something that he repeatedly insisted during the campaign he would not do.

Smith, the MP for Pontypridd, emerged as a challenger after scores of shadow cabinet ministers resigned in the wake of the EU referendum, and Labour MPs overwhelmingly backed a motion of no confidence in their leader.

Rebel MPs must now decide whether to return to the frontline. Many are awaiting the results of a Saturday night meeting of the party’s national executive committee, which will discuss the rules for choosing a future shadow cabinet.

Tom Watson, the party’s deputy leader, has called for a system of elections that would allow MPs to have a say in who serves on Corbyn’s frontbench, and could tempt back some who resigned over the summer.

Any agreed rule changes could be ratified by conference, but Corbyn’s team believes it can beef up the shadow cabinet without the need for elections and would like to see the question discussed alongside other issues, including how to give the membership more of a say in policymaking.

Party sources said talks involving the chief whip, Rosie Winterton, had taken place and would continue later in the day to try to reach a consensus on shadow cabinet elections.

John McDonnell, Corbyn’s campaign director, said the leader’s team hoped to work with MPs from across the party, but would be happy if those critical of his leadership wanted to campaign on issues from the backbenches, citing Yvette Cooper’s role in fighting for support for refugees.

Len McCluskey, the general secretary of the Unite union and a key Corbyn backer, said MPs must fall into line. “We urge Labour MPs to heed the signal sent by the members, twice now in one year, about the direction they want for the party. This includes respecting and supporting the elected leader and his team; no more sniping, plotting and corridor coups,” he said.

Jon Ashworth, the Leicester South MP and shadow cabinet member who sits on the NEC, said: “We have got to unite, but we have also got to recognise that substantial numbers of people didn’t vote for Jeremy.”

He said a deal on shadow cabinet elections would help Corbyn to beef up his frontbench team. “If we want a fully functioning frontbench, we need a way of bringing colleagues back. Various shadow teams have not got their full complement. This seems to me to be a way of doing that.”

In Corbyn’s acceptance speech he promised that attacking Theresa May’s plan to bring back grammar schools would be at the heart of his effort to reunite Labour.

“This time next week we will hit the streets united as a party. I am calling on Labour party members to join us in a national campaign for inclusive education for all next Saturday,” he said.

Addressing the party’s annual women’s conference late on Saturday afternoon, Corbyn called for Labour to unite in the name of Jo Cox, the MP who was killed during the EU referendum campaign.

The Labour leader said that Cox’s death was a “murder of democracy”, adding: “She was adamant that there was much more that united than divides us and there is no better way to honour her memory than ensuring we reunite and we are resolute in making the world a better place.”

Cox nominated Corbyn for the leadership in 2015 but later wrote of her regret, claiming that he was a weak leader with poor judgement.

Corbyn also offered his backing to the MP for Rotherham, Sarah Champion, who has been embroiled in a public row with her former husband in recent days.

The Conservatives, meanwhile, launched a multimedia campaign highlighting the divisions in the Labour party with the slogan: “We have a winner, but it isn’t Britain.”

Tory chairman Patrick McLoughlin said: “Labour are too divided, distracted and incompetent to build a country that works for everyone. Instead of learning lessons from the past, they have engaged in a bitter power struggle that will continue even after they’ve picked a leader.”

Momentum rally celebrates: ‘Corbyn can win’

The room in Liverpool erupted in screams, cheers and dancing as Corbyn was re-elected leader of the Labour party by a larger margin than last year.

This was not the scene of the formal announcement, but about 15 minutes’ walk down the road, where 750 of the leader’s staunch supporters gathered in a community space called Black-E. They were at the World Transformed festival, set up by Momentum, the grassroots group that has been closely involved in Corbyn’s campaign.

Dozens were kitted out in Team Corbyn or Momentum T-shirts. Others also wore their politics on their chests with slogans urging an end to the siege in Gaza and justice for the families of those who have died in police custody.

For the most part, however, those who had turned up to watch Corbyn’s victory were not diehard or longstanding activists. Roisin Vere, 27, and Tom Logan, 29, both live in the city and were planning to go to watch a football match rather than hang around at a political conference.

“It’s the first time in our lives that we’ve had someone in politics who represents our beliefs,” said Vere, who was a Labour and sometimes Green voter before joining as a member. Logan likened it to watching politics come out of the dark ages.

Lucy Page, 50, was another relatively new member. Also from Liverpool, she said she had always admired Corbyn since seeing him on television opposing the war in Iraq during Tony Blair’s leadership.

“I joined the Labour party last year to support him. I’m impressed by the membership numbers and the way he has stood up to the Tories, getting them to stop so many things. I think he can win, but I think the media and the MPs are doing a great disservice to him and the country,” she said.

As the crowd warmed up for Corbyn’s expected victory, a choir from Liverpool Socialist Singers sang a song about being part of Momentum.

Stalls sold Corbyn-related merchandise and books about socialism. Later there would be sessions about “brandalism”, challenging the corporate takeover of communal space, and a panel discussing public ownership.

The atmosphere became electrified when the BBC news channel appeared on a big screen showing videos of the candidates, attracting boos at a mention of Smith’s career in big pharma and cheers for the leader. Chants of “Jeremy, Jeremy” and “Corbyn, Corbyn” broke out in different parts of the room.

Silence descended as Paddy Lillis, the chair of the NEC, read out the result. At the confirmation Corbyn had won, there was a burst of jubilation. A group of middle-aged men in suits in the front row jumped around, while two women waving Momentum T-shirts danced as the cameras snapped.

As a poet performed verse about Corbyn’s treatment by the media, Majid Mehdizadeh, 26, said he was pleased with the result because he admired the leader’s principles and honesty.

“I’ve never see a single interview where he has dodged the question. I joined after Ed Miliband lost last year, but before Jeremy Corbyn … I voted for him then and I voted for him again,” he said.